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Indirect Lyapunov Method for Autonomous Dynamical Systems

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Qualitative and Quantitative Analysis of Nonlinear Systems

Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 111))

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Abstract

In this chapter we establish indirect Lyapunov method for autonomous dynamical systems. Section 9.1 devoted to the first order autonomous differential-operator equations and inclusions. In Sect. 9.2 we consider the second order autonomous operator differential equations and inclusions. In Sect. 9.3 we examine examples of applications. In particular, a model of combustion in porous media; a model of conduction of electrical impulses in nerve axons; viscoelastic problems with nonlinear “reaction-displacement” law etc.

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Notes

  1. 1.

    This section is based on results of [22] and references therein.

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  1. Igor Sikorsky Kyiv Polytechnic Institute, Kyiv, Ukraine

    Michael Z. Zgurovsky

  2. Institute for Applied System Analysis, Igor Sikorsky Kyiv Polytechnic Institute, Kyiv, Ukraine

    Pavlo O. Kasyanov

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  1. Michael Z. Zgurovsky
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  2. Pavlo O. Kasyanov
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Correspondence to Michael Z. Zgurovsky .

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Zgurovsky, M.Z., Kasyanov, P.O. (2018). Indirect Lyapunov Method for Autonomous Dynamical Systems. In: Qualitative and Quantitative Analysis of Nonlinear Systems. Studies in Systems, Decision and Control, vol 111. Springer, Cham. https://doi.org/10.1007/978-3-319-59840-6_9

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